## Work Done by a Force

A force is done whenever the point of application of the force moves in the direction of the force. If a force pushes a block then the block does work. The work done by the force however is not in general to the force multiplied by the distance. Only that component of the force in the direction of the distance moved actually does work.

Example: When a force pushes a block along a surface. The work done by the force F below is W=Fd.

The force and the distance act along the same line. If the do not, then the work done by the force is not Fd. We must resolve the force into components and consider only that component in the direction of the distance moved.

Example: The horizontal force F below does not act along the line of the distance moved d.

We must consider only that component of the force acting up the slope.

The component of the force acting in the direction of the distance move is Fd cos %theta .

This is perhaps made a bit more obvious in the diagram below.

When a force acts so that motion in a circle is produced no work is done by the force, because the body in motion does not move in the direction of the force and can be thought of as a consequence of the fact that the radius of a circle is perpendicular to the tangent at the point where they meet.